/categories route gives me always 404

I'm a newbie to REST and the Slim framework, so I have a very
dummy question I think!
I'm building a really easy PHP webservice that exposes some tables
of a MySQL DB.
One table is called "categories", so I have a route "/categories"
that returns an XML list of the categories inside that table.
I have got problems just with the route.

This is my index.php running on PHP 5.3.8 on my website (just a
test):

The problem seems like it would be a .htaccess problem. I think
you're right. Try to rule out .htaccess issues first. I'm fairly
certain it isn't a Slim issue, but I'll check after work today just
to make sure. Will post again this evening.

Thank you lots for your answer, Josh.
I made some other tests, but unfortunately I'm not an Apache expert
:(
I can't figure it out since it seems to "like" some urls and
"dislike" others... for instance I can't make /categories and
/shops work, while /payments works well... a really strange
behaviour I think!

I tried not to use .htaccess by renaming it to htaccess.txt,
then I used the no-rewrite URL by calling: